Pith Number

pith:YQRD6N2K

pith:2012:YQRD6N2KKG3PMWV3KGOCHMYQN7

not attested not anchored not stored refs pending

Ore's Conjecture for $k=4$ and Gr\" otzsch Theorem

Alexandr Kostochka, Matthew Yancey

arxiv:1209.1173 v1 · 2012-09-06 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YQRD6N2KKG3PMWV3KGOCHMYQN7}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:46:06.350857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4223f374a51b6f65abb519c23b3106fdd0c97bd086db15f4749da322b30ad73

Aliases

arxiv: 1209.1173 · arxiv_version: 1209.1173v1 · doi: 10.48550/arxiv.1209.1173 · pith_short_12: YQRD6N2KKG3P · pith_short_16: YQRD6N2KKG3PMWV3 · pith_short_8: YQRD6N2K

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YQRD6N2KKG3PMWV3KGOCHMYQN7 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c4223f374a51b6f65abb519c23b3106fdd0c97bd086db15f4749da322b30ad73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3644a184353d80e33c7f77cd1f88464514ad85255ef5fb01c16f8248e220a8d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-06T04:14:38Z",
    "title_canon_sha256": "9b205df937c17f0b3ee2e9d167247d32201245056df731e89526e14b04cd3f8c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1173",
    "kind": "arxiv",
    "version": 1
  }
}